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George Ford added a couple of penalties at the start of the second half to keep Bath in the game, but two misses prevented the fly-half from drawing his team level.
Sale were reduced to 14 men late on when Michael Paterson was sent to the sin bin, but Bath were unable to capitalise on their numerical advantage.
The hosts had chances to extend their lead late on, but Cipriani and substitute Joe Ford failed to split the uprights.
The result leaves Sale sixth in the table.